Addition and subtraction with negative numbers means that operation involves movement or direction on a number line, and subtracting a negative number is the same as adding a positive number.
Contents
Key Points to Remember
- Addition
- Addition is commutative. This means that the order in which you add a pair of numbers does not make a difference, e.g., 3 + 5 = 5 + 3.
- The addends are the individual numbers you add together.
- The sum is the answer when two or more numbers are added together.
- Subtraction
- Subtraction is NOT commutative. This means that the order in which you subtract a pair of numbers does make a difference, e.g., 5 – 3 ≠ 3 – 5.
- The minuend is the starting number that is being subtracted from.
- The subtrahend is the number that is being taken away.
- The difference is the final result.
- Calculations can be written with brackets around negative numbers because this can make a calculation easier to read, e.g., -3 + -1 is the same calculation as (-3) + (-1), and 5 + -3 is the same as 5 + (-3).
- Learning about positive and negative numbers will help when adding and subtracting negative numbers.
- Use the Commutative Property of Addition and the Distributive Property of Multiplication when applicable.
Core Rules
- Start point: The first number in your equation is your starting position on the number line.
- Adding a positive: Move to the right (increasing value) on the number line.
- Adding a negative: Move to the left (decreasing value) on the number line or think of it as adding a debt.
- Subtracting a negative: Two negative signs right next to each other cancel out and become a plus sign (moving to the right on the number line).
Adding Positive and Negative Numbers
Adding Positive Numbers
Just find the sum. (Also see the Commutative Property of Addition.)
4 + 5 = 5 + 4 = 9
Adding Positive and Negative Numbers
Adding a negative number to a positive number is the same as subtraction. (Also see Negative Numbers Using a Number Line, the Commutative Property of Addition and Addition of Positive and Negative Numbers Using Absolute Values.)
(-3) + 5 = 5 + (-3) = 5 – 3 = 2
(-6) + 1 = 1 – 6 = (-5)
Adding Negative Numbers
Just find the sum. (See the Negative Numbers Using a Number Line, the Commutative Property of Addition, and the Distributive Property of Multiplication.)
(-7) + (-4) = (-4) + (-7) = -1 × (4 + 7) = -1 × (11) = (-11)
Subtracting Positive and Negative Numbers
Subtracting a negative is the same as adding. (See the Negative Numbers Using a Number Line, the Addition of Positive and Negative Numbers Using Absolute Values, and Keep, Change, Change.)
9 – 2 = 9 + (-2) = 7
4 – 7 = 4 + (-7) = -3
6 − (−3) = 6 + 3 = 9
(-2) – (-9) = (-2) + 9 = 9 + (- 2) = 9 – 2 = 7
(-8) – 3 = (-8) + (-3) = 11
Notes
Addition of Positive and Negative Numbers Using Absolute Values
Another way to add a positive and a negative number is to subtract the addend with the smaller absolute value from the addend with the larger absolute value and keep the sign of whichever addend had the larger absolute value.
(−8) + 5: |−8| > |5|, so answer is negative → −(8−5) = −3
(−3) + 9: |9| > |−3|, so answer is positive → +(9−3) = 6
Negative Numbers (Google Slides)
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Negative Numbers Using a Number Line
Addition
The number line is a visual tool for adding real numbers, including integers, fractions, and multi-digit values. To use it, mark the first number and move right for positive values or left for negative ones based on the second number. This method effectively demonstrates arithmetic operations, such as 4 + 5 = 9 or (-12) + 7 = (-5). For large numbers, decompose them into smaller units to simplify the process.
See Addition on a Number Line.
Subtraction
Subtraction on a number line helps calculate the difference between integers, fractions, and decimals by locating the minuend and moving back based on the subtrahend. For positive numbers, you move left; for negative numbers, operations shift toward addition. Open number lines are used for larger 2-digit and 3-digit problems by breaking the subtrahend into hundreds, tens, and ones, then performing sequential jumps to arrive at the final result.
See Subtraction on a Number Line.
Videos
References
Pierce, Rod. “Adding and Subtracting Positive and Negative Numbers.” Math Is Fun, 2025. https://www.mathsisfun.com/positive-negative-integers.html.
“Number Line Addition – Examples and Diagrams.” Math Monks, April 26, 2023. https://mathmonks.com/number-line/addition-on-a-number-line.
“Subtraction on a Number Line with Integers, Decimals, and Fractions.” Math Monks, April 3, 2023. https://mathmonks.com/number-line/subtraction-on-a-number-line.
“What Are Positive and Negative Numbers.” BBC Bitesize, November 4, 2021. https://www.bbc.co.uk/bitesize/topics/zp26n39/articles/zbpbbqt.
“KS3 Maths: How to Add and Subtract Positive and Negative Numbers.” BBC Bitesize, September 8, 2021. https://www.bbc.co.uk/bitesize/topics/zp26n39/articles/zrjsn9q.
“Negative Numbers – Add, Subtract, Multiply and Divide.” SolveCalc, n.d. Accessed September 5, 2026. https://solvecalc.net/negative-numbers.
Zegarelli, Mark. “Addition and Subtraction with Negative Numbers.” Dummies, March 26, 2016. https://www.dummies.com/article/academics-the-arts/math/basic-math/addition-and-subtraction-with-negative-numbers-150568/.
“Adding and Subtracting Negative Numbers – Steps, Examples & Worksheet.” Third Space Learning, August 10, 2021. https://thirdspacelearning.com/gcse-maths/number/adding-and-subtracting-negative-numbers/.
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